1- Determine the logic equation for the output and construct the truth table and Karnaugh maps for the multiplexer shown below: Do D1 Y D2 D3 So E 2- Use a 4-to-1 multiplexer and logic gates to implement the function:
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- A circuit which takes a binary-coded decimal (BCD) number as input s to be designed such that the single output Q is true if the input is a prime number (remerber that 0 and 1 count as prime numbers). (a)Draw a truth table that specifies the above circuit (b)Using the truth table you have constructed and the Karnaugh map method find the minimised Boolean expression for the output Q. (c)Implement the digital circuit using the minimum number of 2-input logic AND, OR gates and inverters (NOT.Design a 4-bit arithmetic circuit, with two selection variables S1 and S0, that generates the arithmetic operations in the following table. Draw the logic diagram for a single bit stage. Note that B’ represents “Not B”. Draw the logic diagram for a single bit stagUsing a 4-bit signed input P=P3P2P1P0 and a control input Z, use a 4-bit adder and any logicgates to design a digital circuit that does the following: ● Outputs P + 3, if the input Z = 0● Outputs P − 3, if the input Z = 1 You can ignore cases where an overflow* might occur after performing the addition or subtraction operation, as long as the circuit performs the signed binary arithmetic correctly. *In computers, typically there is additional circuitry for an overflow flag that gets triggered when the result of an arithmetic operation “does not fit” the number of bits allocated for the output. Please ensure that your components, such as your 4-bit adder are shown clearly with the complete labels of their input and output pins and signals. The sample diagram below shows examples of these labels.
- A combinational logic circuit that compares between two 2-bit numbers A (A1 A0) and B(B1 B0) is designed. Output F is high when ? > ? and low when ? < ?. 1) Are there any undefined outputs? If there are any undefined outputs what are the inputs?Given the logic function: F(A,B,C,D) = Σm(0,4,5,10,11,13,14,15) a. Find a minimum circuit which implements F using AND and OR gates. Identify two 1-hazards in the circuit. b. find another minimum circuit which implements F using AND and OR gates. Identify two 0-hazards in the circuit. c. Find an AND-OR circuit for F which has no hazards.Implement the following logic function using only 3-8 decoders and logic gates. ?(?,?,?,?)= Σ?(2,4,6,8,10,14,15)
- Using the analysis technique where you first extract the truth table and then use it to derive the output’s logic expression, analyze the circuit. Record your results below. I added the circuit as an image Conclusion In your own words, describe the process used to analyze a logic circuit where you first extract a truth table and then derive the logic expression. 2.Again, in your own words, describe the process used to analyze a logic circuit where you first extract the logic expression and then derive the truth table.Logic Function F (x, y, z, w) = ∑ m (0,2,4,6,10,13) + ∑ k (8,12) as sum of minimers are given. (Note: There are terms that are not taken into account.) a. Obtain the Truth Table. b. Simplify with the Karnough Map approach. c. Draw the simplified Logic circuit with two input AND-NOT (NAND) gates. How many elements you realized, what is your gain? Comment.Which of the following statements accurately represents the best method of logic circuit simplification? a. Actual circuit trial and error evaluation and waveform analysis b. Boolean algebra and actual circuit trial and error evaluation c. Karnaugh mapping and circuit waveform analysis d. Karnaugh mapping and Boolean algebra
- 1-Using the Karnaugh Method, design and draw the circuit of the logic circuit that gives the result of the multiplication of the two-bit numbers "AB" and "CD" according to minterms (SOP). Do not make any further simplifications before or after the Karnaugh Method. In tables and Karnaugh, ensure that the least significant bit is on the far right and the entries are sorted alphabetically. Make sure that the circuit you have drawn is understandable, the function you have written and the truth table are readable.3) Logic Function F (x, y, z, w) = ∑ m (0,2,4,6,10,13) + ∑ k (8,12) as sum of minimers is given a) Obtain the Truth Table. b) Simplify with the Karnough Map approach. c) Draw the simplified Logic circuit with two input AND-NOT (NAND) gates. With how many apples you realized, what is your gain? Comment.4.1 Investigate if the following Boolean “identity” is correct, or not. If it is not correct, formulate the correct version of the identity (?′?+?)′=?+?′?′. [2]4.2 Use the identities of Boolean algebra to verify the following identity: [4]?(?+?)+??′+??′+?=?+?+?4.3 Consider the logic gate circuit below:a) Formulate the Boolean expression corresponding to the output of the logic circuit diagram above. [2]b) Hence, show that the Boolean expression formulated in part (a) reduces to ??+?. [3]c) Draw the logic gate circuit diagram corresponding to the reduced expression inpart (b) above. 3.1 Let r, s, t denote the statements “Joe is registered for MCI511S”, “Joe will go to the zoo next week”, “Joe is registered for PBT512S”, respectively. Translate the symbolic statement (∼?∨?)→∼? into words. [2]3.2 Write the negation of the statement “If Joe writes the exam, he will go the airport but he will not catch the flight”. [2]3.3 Determine the truth value of the compound statement (?∧∼?)∨∼?, if p…